Does a shield +X give the +X bonus without wielding it?

[Trafalgar]

This is actually covered in the Sage Advice Compendium (p21):

Can you gain the magical bonus of a +2 shield if you are holding the shield without taking an action to don it?

Yes, but only the magical +2, which you gain while holding the shield. In contrast, you gain the shield’s nonmagical AC bonus only if you use your action to don the shield as normal (see “Getting Into and Out of Armor” in chapter 5 of the Player’s Handbook).

Does this mean I get the AC bonus for a Ring of Protection if I am holding it in my hand but I am not wearing it on my finger? No because RAW specifically prohibits it.

That's a weird ruling. Sometimes I think J. Crawford makes these rulings while tweeting under the influence but forgets to delete the tweet when he sobers up.